When electrons tunnel through a double-barrier structure, there exists a region of bistability (or tristability) in the current-voltage characteristics due to the dynamical charge feedback effect in the resonant well. We propose a mechanism of acoustic-phonon-assisted tunnelling to explain the experimentally observed non-monotonic behaviour of the width of the tristable region. It is found that this width has a single maximum as experimentally observed. Furthermore, contrary to the previous proposal, our result shows that electron thermal activation is not the dominant mechanism in controlling this temperature-dependent width.